In this article, examples are shown to demonstrate how open-ended mathematical activities can be used in the classroom. Open-ended activities give students opportunities to apply their understanding in unfamiliar contexts without the pressure of finding one perfect solution.

Research confirms that critical thinking plays a fundamental role in decision making and problem solving, skills that are essential to function as successful adults in a complex world. Consequently, it has been a focus of educational research for decades. Faculty meetings and teacher training sessions repeatedly run sessions on ways that teachers…

Analogical reasoning is a core facet of higher cognition in humans. Creating analogies as we navigate the environment helps us learn. Analogies involve reframing novel encounters using knowledge of familiar, relationally similar contexts stored in memory. When an analogy links a novel encounter with a familiar context, it can aid in problem…

Only knowledge is not sufficient to make students succeed in the world. Students need to attain 21st century skills like problem-solving, creativity, innovation, metacognition, communication etc. to endure in the modern world. Problem-solving skill is one of the fundamental human cognitive processes. Whenever students face a situation where they…

How do scientists make inferences for something they cannot directly observe? The Black Box approach seems ideal to help students understand how scientists work. Black Boxes are sealed units; their interior is not accessible. The effort to determine their possible content (internal structure) demands successive modifications in hypothesis,…

Peter Dunn and Margaret Marshman present the second of their data files articles in which they discuss the statistical investigation cycle which describes the whole process of conducting a statistical research study. [For "The Data Files: A Series of Articles to Support Mathematics Teachers to Teach Statistics," see EJ1259108.]

This article is based on classroom application of a problem story constructed by Amos Tversky in the 1970s. His intention was to evaluate human beings' intuitions about statistical inference. The problem was revisited by his colleague, the Nobel Prize winner Daniel Kahneman. The aim of this article is to show how popular science textbooks can…

In this article, Strayer and Matuszewski present a six-phase strategy that teachers can use to help students develop a conceptual understanding of inferential hypothesis testing through simulation. As Strayer and Matuszewski discuss the strategy, they describe each phase in general, explain how they implemented the phase while teaching their…

The purpose of this paper is to provide an easy template for the inclusion of the Bayes factor in reporting experimental results, particularly as a recommendation for articles in the "Journal of Problem Solving." The Bayes factor provides information with a similar purpose to the "p"-value--to allow the researcher to make…

Researchers and teachers often recommend motivating exercises and use of mathematics or statistics software for the teaching of basic courses in probability and statistics. Our courses are given to large groups of engineering students at Lund Institute of Technology. We found that the mere existence of real-life data and technology in a course…

This paper briefly discusses four measurement challenges of data science or "big data" in educational assessments that are enabled by technology: 1. Dealing with change over time via time-based data. 2. How a digital performance space's relationships interact with learner actions, communications and products. 3. How layers of…

The importance of mathematical visual images is indicated by the introductory paragraph in the Statistics and Probability content strand of the Australian Curriculum, which draws attention to the importance of learners developing skills to analyse and draw inferences from data and "represent, summarise and interpret data and undertake…

Developing critical thinking since the educational revolution gave rise to flourishing movements toward embedding critical thinking (CT henceforth) stimulating classroom activities in educational settings. Nevertheless the process faced with complications such as teachability potentiality, lack of practical frameworks concerning actualization of…

This important new book identifies the skills and qualities students need, based on the Common Core State Standards, to be "really" ready for college and careers. Go beyond content knowledge...the deep thinking and learning skills detailed in this book will equip students for success! Prepare your students for their futures by helping them become:…

If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…